A body of mass 0.5 kg released from a height of 3mcalculate potential and kinetic energy when it is at a height of 2m from the ground
To calculate the potential and kinetic energy of the body when it is at a height of 2m from the ground, we need to consider the conservation of mechanical energy.
The potential energy of an object is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
The kinetic energy of an object is given by the formula KE = 1/2mv^2, where m is the mass and v is the velocity.
Initially, when the body is at a height of 3m from the ground, the potential energy is:
PE = mgh = 0.5 kg * 9.8 m/s^2 * 3m = 14.7 Joules.
The body is then released and falls to a height of 2m from the ground.
The change in potential energy can be calculated as:
ΔPE = mgh2 - mgh1 = 0.5 kg * 9.8 m/s^2 * (2m - 3m)
ΔPE = -4.9 Joules.
The change in potential energy is negative because the body is losing potential energy as it falls.
Assuming no energy is lost due to air resistance or other non-conservative forces, the change in potential energy must be equal to the change in kinetic energy.
Therefore, the kinetic energy when the body is at a height of 2m from the ground is:
KE = ΔPE = -4.9 Joules.
Note that the negative sign indicates that the kinetic energy is negative, meaning the body is moving in the downward direction.
To calculate the potential and kinetic energy of the body when it is at a height of 2m from the ground, we need to use the equations for potential energy and kinetic energy.
1. Potential energy:
Potential energy is given by the equation: Potential Energy = mass × gravitational acceleration × height.
Let's substitute the given values into the equation:
Potential Energy = 0.5 kg × 9.8 m/s^2 × 2 m
Potential Energy = 9.8 Joules
2. Kinetic energy:
Kinetic energy is given by the equation: Kinetic Energy = (1/2) × mass × velocity^2.
Since the body is dropped from rest, the velocity can be calculated using the equation: Velocity = sqrt(2 × gravitational acceleration × height).
So, let's calculate the velocity first:
Velocity = sqrt(2 × 9.8 m/s^2 × 3 m)
Velocity = sqrt(58.8) ≈ 7.67 m/s
Now, we can calculate the kinetic energy using the velocity:
Kinetic Energy = (1/2) × 0.5 kg × (7.67 m/s)^2
Kinetic Energy = 2.33 Joules
Therefore, when the body is at a height of 2m from the ground, its potential energy is 9.8 Joules and kinetic energy is 2.33 Joules.